What does it mean to understand something? Is it the ability to transfer a working knowledge of a set of principles from the environment in which it was introduced to a new environment? Is it the mastery of a set of tasks? From my own experiences I think there is validity in all of these definitions, as well as many more which tend to come up in conversations on this topic.
I would even go so far as to say that the lack of a singular common definition lends evidence to my theory that the meaning of understanding is not singular and is constantly being mediated between those in the conversation. From this description I derive my own definition of understanding: the act of translating one's thoughts and / or actions in such a way that multiple parties can find common ground. For example: I say the word 'work', how do I or anyone else know if I understand this concept? In talking with other people, drawing from previous experiences, and making additional observations I can work to find enough common ground with other people on the meaning of 'work', at least in a specific context, that I can say I understand 'work'. Understanding in this sense is the mediating of a conceptual common ground.
To me then teaching is the process of helping my students understand how to think scientifically and communicate both in standard language and with mathematics. I want my students to understand how 'the truth' is not some abstract ideal but a set of common and reproducible observations, and it comes about from being systematic about one's observations, record-keeping, and communications. The Universe is ultimately indifferent to what you want to be true, and what turns out to be the case is often a best-guess, a concession towards present limitations. Though if the conversation and investigation is interesting in of itself it is worth doing. Why else practice science and its teaching?
Collaborators
Ariel Levi Simons
Teaching Philosophy
What does it mean to understand something? Is it the ability to transfer a working knowledge of a set of principles from the environment in which it was introduced to a new environment? Is it the mastery of a set of tasks? From my own experiences I think there is validity in all of these definitions, as well as many more which tend to come up in conversations on this topic.
I would even go so far as to say that the lack of a singular common definition lends evidence to my theory that the meaning of understanding is not singular and is constantly being mediated between those in the conversation. From this description I derive my own definition of understanding: the act of translating one's thoughts and / or actions in such a way that multiple parties can find common ground. For example: I say the word 'work', how do I or anyone else know if I understand this concept? In talking with other people, drawing from previous experiences, and making additional observations I can work to find enough common ground with other people on the meaning of 'work', at least in a specific context, that I can say I understand 'work'. Understanding in this sense is the mediating of a conceptual common ground.
To me then teaching is the process of helping my students understand how to think scientifically and communicate both in standard language and with mathematics. I want my students to understand how 'the truth' is not some abstract ideal but a set of common and reproducible observations, and it comes about from being systematic about one's observations, record-keeping, and communications. The Universe is ultimately indifferent to what you want to be true, and what turns out to be the case is often a best-guess, a concession towards present limitations. Though if the conversation and investigation is interesting in of itself it is worth doing. Why else practice science and its teaching?